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A new and systematic basic approach to force- and vision-based robot manipulation of deformable (non-rigid) linear objects is introduced. This approach reduces the computational needs by using a simple state-oriented model of the objects. These states describe the relation between the deformable and rigid obstacles, and are derived from the object image and its features. We give an enumeration of possible contact states and discuss the main characteristics of each state. We investigate the performance of robust transitions between the contact states and derive criteria and conditions for each of the states and for two sensor systems, i.e. a vision sensor and a force/torque sensor. This results in a new and task-independent approach in regarding the handling of deformable objects and in a sensor-based implementation of manipulation primitives for industrial robots. Thus, the usage of sensor processing is an appropriate solution for our problem. Finally, we apply the concept of contact states and state transitions to the description of a typical assembly task. Experimental results show the feasibility of our approach: A robot performs several contact state transitions which can be combined for solving a more complex task.